Dynamic Stability Analysis of Cages in High-Speed Oil-Lubricated Angular Contact Ball Bearings

To investigate the cage stability of high-speed oil-lubricated angular contact ball bearings, a dynamic model of cages is developed on the basis of Gupta’s and Meeks’ work. The model can simulate the cage motion under oil lubrication with all six degrees of freedom. Particularly, the model introduces oil-film damping and hysteresis damping, and deals with the collision contact as imperfect elastic contact. In addition, the effects of inner ring rotational speed, the ratio of pocket clearance to guiding clearance and applied load on the cage stability are investigated by simulating the cage motion with the model. The results can provide a theoretical basis for the design of ball bearing parameters.

Air flow patterns and noise analysis inside high speed angular contact ball bearings

The vortex formed around the rolling ball and the high pressure region formed around the ball-raceway contact zone are the principle factors that barricades the lubricant entering the bearing cavity, and further causes improper lubrication. The investigation of the air phase flow inside the bearing cavity is essential for the optimization of the oil-air two-phase lubrication method. With the revolutionary reference frame describing the bearing motion, a highly precise air phase flow model inside the angular contact ball bearing cavity was build up. Comprehensive factors such as bearing revolution, ball rotation, and cage structure were considered to investigate the influences on the air phase flow and heat transfer efficiency. The aerodynamic noise was also analyzed. The result shows that the ball spinning leads to the pressure rise and uneven pressure distribution. The air phase velocity, pressure and cage heat transfer efficiency increase as the revolving speed increases. The operating noise is largely due to the impact of the high speed external flow on the bearing. When the center of the oil-air outlet fixes near the inner ring, the aerodynamic noise is reduced. The position near the inner ring on the bigger axial side is the ideal position to fix the lubricating device for the angular contact ball bearing.

Quasi Dynamic Calculation of Local Stiffness of Angular Contact Ball Bearings

In order to describe the performance of thin wall bearing on rotor system more accurate,the simplified model of bearing local stiffness was proposed. The load distribution and local contact deformation in angular contact ball bearings were calculated using quasi dynamic calculation method. Based on the relationship of local load to contact deformation,the calculation model of local bearing stiffness was subsequently built to get radial and axial components of local stiffness. Effects of external loads on the local bearing stiffness were analyzed. The results showed that local stiffness in bearings is symmetric to the axis of radial load,and its value has a maximum on the symmetry axis along the radial load direction. External radial and axial load have different effects on local bearing stiffness.

Dynamic Analysis of Flexible Cage of High-speed Angular Contact Ball Bearing

A dynamics formula was established for the flexible cage of high-speed angular contact ball bearing. A modified Craig-Bampton component mode synthetic method was used to establish the formula with regard to the flexibility of cage and based on a dynamic analysis of angular contact ball bearing,and a rigid-flexible multi-body dynamic analysis program was developed using ADAMS,which is verified by a computation example of Gupta. The results show that it's not likely to keep the rotation smoothness of cage when the ratio of pocket clearance to guiding clearance and the ratio of radial load to axial load become too large or too small. By comparison,the flexible cage runs more smoothly than the rigid cage.

Rolling contact fatigue of silicon nitride bearing balls under pure rolling condition

A newly developed pure rolling fatigue test rig with three contact points for bearing bails was used to perform rolling contact fatigue （RCF） tests. The fatigue properties of GCrl5 steel bails and two kinds of Si3N4 ceramic balls （GSN-200 and NBD-200） produced with different technologies were compared. Ball surfaces were examined after failure with optical microscope and scanning electron microscope （SEM）. It was identified by tests that the failure mode of ceramic balls was surface spail. The main factor of ceramic bail failure was principal tensile stress. Life tests data, summarized in accordance with the Weibull theory, showed that the life of GSN-200 balls was close to that of GCrl5 balls, whereas the life of NBD-200 balls was much longer than those of GSN-200 and GCr15. Under the same working condition, the temperature rise of all ceramic bails was lower than that of steel balls, and their crack propagation rates were slower than that of steel balls.

Contact Force Distribution and Static Load-carrying Capacity of Large Size Double Row Four-point Contact Ball Bearing

Clearance not only affects the startup torque,rotation precision and stiffness of bearing,but also affects the load distribution,load-carrying capacity and life of bearing.A computational model in which the clearance of bearing is first included is presented for determining the contact force distribution and static load-carrying capacity of a double row four-point contact ball bearing which is subjected to the combined radial,axial and overturning moment loadings.The relation between the negative axial clearance and the contact force distribution is analyzed.The static load-carrying capacity curves are established,and the effects of the changes in negative axial clearance,curvature radius coefficient of raceway groove and initial contact angle on the static load-carrying capacity are analyzed.The results show that,with the increase in the absolute value of negative clearance,the maximum contact load decreases first and then increases.The clearance values in the range of 0.2 mme0 mm have little effect on the static load-carrying capacity of bearing.With the increase in the curvature radius coefficient of raceway groove and the decrease in the initial contact angle,the static load capacity of bearing decreases.

Bifurcation of Periodic Motion of Rigid Rotor System Supported by Angular Contact Ball Bearings

Rotor systems supported by angular contact ball bearings are complicated due to nonlinear Hertzian contact force. In this paper, nonlinear bearing forces of ball bearing under five-dimensional loads are given, and 5-DOF dynamic equations of a rigid rotor ball bearing system are established. Continuation-shooting algorithm for periodic solutions of the nonlinear non-autonomous dynamic system and Floquet multipliers of the system are used. Furthermore, the bifurcation and stability of the periodic motion of the system in different parametric domains are also studied. Results show that the bifurcation and stability of period-1 motion vary with structural parameters and operating parameters of the rigid rotor ball bearing system. Avoidance of unbalanced force and bending moment, appropriate initial contact angle, axial load and damping factor help enhance the unstable rotating speed of period-1 motion.

Modeling and Experiment on Contact Stiffness and Accuracy Analysis of Ball Linear Guide Feed Unit

The contact stiffness and the error analysis have an important effect on the manufacture and the optimization of Ball Linear Guide Feed Unit( BLGFU). In order to analyze the contact stiffness and linear errors or angle errors of BLGFU,in this paper,the contact stress and deformation mechanics between the ball and rail is analyzed. Based on Hertz theory of contact and theory of the multi-body system,a model of the contact stiffness considering the changes in contact angle is established. With the increasing of the external load,the varying trend of the contact deformation can be obtained. Therefore, the motion accuracy degradation of the BLGFU can be analyzed. By using a special experimental device and test system of the rolling linear guide worktable,the horizontal contact stiffness and the vertical linear stiffness are obtained,respectively. By comparing the contact stiffness of the experiment dates and the simulation results,the variation tendency of two curves is consisted and the difference between the measured values and the theoretical values is less than 18%. It is obvious that the model of the contact stiffness considering changes of contact angle has accuracy and feasibility. Thus,while external force point locating at different positions; the contact stiffness and the accuracy analysis of the BLGFU are proved validity by simulations.

Modeling approach for axial contact stiffness of ball screws

Axial stiffness of ball screws has great effects on accuracy of positioning,dynamic characteristic and transmission efficiency. Axial contact stiffness modeling of ball screws is the key problem in dynamic analysis of ball screws. Aiming at obtaining axial stiffness of ball screws considering microscopic fractal characteristics of contact surfaces,a new analytical method is proposed to estimate axial contact stiffness of ball screws and combine the minimum excess principle with Mandelbort( MB)fractal theory in this research. The minimum excess principle is employed to conduct normal stress analysis. And the Mandelbort fractal theory is adopted to obtain contact stiffness in ball screws. The effectiveness of the proposed method is validated by the self-designed experiment. The comparison between theoretical results and experimental results demonstrates that axial contact stiffness of ball screws could be obtained by the proposed method.

A new nonlinear force model to replace the Hertzian contact model in a rigid-rotor ball bearing system

A new nonlinear force model based on experimental data is proposed to replace the classical Hertzian contact model to solve the fractional index nonlinearity in a ball bearing system. Firstly, the radial force and the radial deformation are measured by statics experiments, and the data are fitted respectively by using the Hertzian contact model and the cubic polynomial model. Then~ the two models are compared with the approximation formula appearing in Aeroengine Design Manual. In consequence, the two models are equivalent in an allowable deformation range. After that, the relationship of contact force and contact deformation for single rolling element between the races is cal- culated based on statics equilibrium to obtain the two kinds of nonlinear dynamic models in a rigid-rotor ball bearing system. Finally~ the displacement response and frequency spectrum for the two system models are compared quantitatively at different rotational speeds, and then the structures of frequency-amplitude curves over a wide speed range are compared qualitatively under different levels of radial clearance, amplitude of excitation, and mass of supporting rotor. The results demonstrate that the cubic polynomial model can take place of the Hertzian contact model in a range of deformation.

精密轴系低温动态摩擦力矩波动分析及优化策略

精密轴系作为机械设备旋转支承核心,其动态摩擦力矩及平稳性直接影响整机功耗及运转精度,尤其在低温环境下,由于温度对润滑油黏度、零件尺寸和配合关系的影响,精密轴系更易出现动态摩擦力矩异常波动。针对某精密轴系低温环境下批次性动态摩擦力矩异常波动现象进行了主因素分析,通过ADAMS平台建立仿真模型,分析了引导间隙、兜孔间隙对保持架动态特性的影响。结合拆解数据,指出兜孔间隙不合理引发的兜孔磨损是造成精密轴系动态摩擦力矩异常波动的原因,通过数理统计对保持架参数进行优化,兜孔间隙与引导间隙之比为0.70~0.85时,该精密轴系低温下运转稳定。

考虑弹流润滑效应的三点接触球轴承刚度特性分析

为获得润滑状态下三点接触球轴承更为准确的刚度特性,应考虑弹流润滑效应对轴承刚度的影响。文中基于拟静力学模型考虑高速离心力和陀螺力矩效应,根据给定轴承的结构参数和工况,计算滚动体与内外圈的法向接触载荷和各部件的运动速度。将拟静力学模型的计算结果和润滑介质参数代入弹流润滑模型,求解出滚动体与内外圈之间的压力分布和油膜厚度分布。进一步研究了转速、轴向载荷和润滑油的初始黏度对油膜压力和最小油膜厚度的影响。基于弹流润滑理论分析了转速和轴向载荷对轴承接触刚度、油膜刚度及综合刚度的影响。结果表明:转速的提高会大幅增加润滑油膜的整体厚度;润滑油初始黏度的增大会增加油膜厚度;随着轴承转速的提高,轴承的整体轴向刚度和轴向油膜刚度减小;随着轴向载荷的增大,轴承轴向刚度和轴向油膜刚度增大,且差值变化不大。

石墨烯纳米颗粒参数对角接触球轴承油气润滑特性的影响

为探究高速旋转状态下油气负载石墨烯润滑特性,以B7003C轴承为研究对象,通过有限元软件建立其三相润滑流场的数值模型,考虑石墨烯纳米颗粒参数对润滑的影响,观察润滑油和石墨烯纳米颗粒在轴承腔内的分布和变化,结果表明:轴承腔内石墨烯润滑油的体积随时间延长而增大,一段时间后润滑油总体积与分布状态在轴承腔内随时间脉动循环;石墨烯质量分数增加改变了基础油的润湿性,增大了相同工况下轴承腔内油的含量,进而改善了轴承润滑状态;石墨烯纳米颗粒在轴承腔内的运动轨迹和分布与其粒径尺寸有关,小粒径石墨烯扩散速度更快,主要参与钢球与内沟道润滑,更易从轴承腔入油口一侧溢出;大粒径石墨烯主要参与钢球与外沟道润滑,更易从油气入口侧进入轴承腔内参与润滑。

含石墨烯油气润滑的角接触球轴承腔热流数值分析

为更有效地降低大功率高速电主轴用高速角接触球轴承腔温度,对含石墨烯的油气润滑影响轴承腔热流特性的规律进行分析。基于流体力学守恒方程,建立了高速角接触球轴承腔体内压缩气体、润滑油和石墨烯颗粒形成的气液固三相流热流分析数学模型。通过数值模拟分析了不同速度压缩气体状态下油气通道中的石墨烯润滑油环状流形成条件、轴承腔内石墨烯润滑油流场速度,以及石墨烯颗粒分布与轴承腔温度场的关系。结果表明,石墨烯润滑油速度与压缩气体速度之比为1∶10时,油气通道中会形成石墨烯润滑油环状流,使高速角接触球轴承腔具有良好的润滑效果;高速运转工况下,轴承腔内石墨烯的分布状态同时受离心力与滚珠高速自旋的影响,而且石墨烯颗粒分布越密集,该区域的温度越低;石墨烯润滑油在滚珠与内圈接触区域流速越大,表面换热系数越高,该区域散热越快,为石墨烯油气润滑更好地降低高速角接触球轴承温度、保障轴承正常工作提供了理论依据。

滚动轴承旋转精度测量实验设计

为提升“新工科”专业人才培养质量,满足行业对毕业生解决复杂工程问题能力的要求,以滚动轴承旋转精度测量为例,设计一项包含理论建模、测量数据研究、软件开发的工程实验。基于角接触球轴承旋转精度检测时的接触关系,建立径向跳动值和轴向跳动值计算解析模型。选取9个均布位置检测轴承套圈设计参数,利用傅里叶级数对测量数据进行轮廓拟合,设计旋转精度计算流程并进行编程计算,得出旋转精度变化规律。计算与测试结果一致,遵循国家标准开展实验,与工程问题无缝衔接,实施过程具有创新性,强化实验对人才培养的支撑作用。

考虑内、外圈复合故障的角接触球轴承振动特性研究

为描述考虑内、外圈复合故障角接触球轴承的振动特性,建立了角接触球轴承内、外圈复合故障时变位移激励模型;基于非线性Hertz接触理论,建立了角接触球轴承时变刚度模型;提出了考虑内、外圈复合故障的角接触球轴承动力学计算方法,研究了不同参数和工况条件下复合故障轴承的振动响应规律。研究结果表明:随着故障尺寸和轴承载荷的增大,复合故障轴承的振动特征频率不变,但其幅值增大;随着轴承转速的增大,复合故障轴承的振动特征频率及其幅值均增大;故障位置的变化将对复合故障轴承的振动特征产生很大影响,故障处越接近承载区,轴承的负载越大,振动特征越明显。

喷嘴位置对轴承腔内油气润滑两相流的影响

基于气液两相流理论,采用多重坐标系法构建角接触球轴承数值计算模型,分析不同喷嘴位置和转速下轴承腔内油相体积分数、保持架表面及轴承内外圈的油气分布特性。结果表明:在轴承低转速下,正面供油时轴承腔内油相体积分数及其周向分布的波动大于背面供油;正面供油时保持架下表面会产生润滑油的积聚,造成润滑油无法及时通过出口排出,而背面供油时润滑油在保持架表面的油相分布更均匀;正面供油时内圈左面油相体积分数较高,外圈油相分布变化较大,而背面供油时内圈右面、中间面及外圈中间面油相体积分数较高。不同转速下喷嘴位置对腔内油相分布的影响也不同,低转速下正面供油时腔内油相体积分数更高,高转速下喷嘴位置对轴承腔内油相分布的影响较小,润滑油在轴承腔内分布较为均匀,保持架下侧未见明显的润滑油积聚。

联合载荷作用下精密轴系角接触球轴承钢球与保持架动力学行为分析

针对联合载荷作用下精密轴系角接触球轴承钢球与保持架的相互作用行为,基于滚动轴承动力学理论建立了精密轴系动力学分析模型,分析了转速、载荷、轴承结构参数对钢球与保持架动力学行为的影响,并通过保持架转速试验验证了模型的准确性,结果表明:力矩载荷对钢球与保持架动力学行为的影响程度较径向载荷明显;在径向载荷作用下,当转速小于40000 r/min时钢球与保持架的作用力随轴向预紧力增大而增大,当转速大于40000 r/min时钢球与保持架的作用力随轴向预紧力增大先减小后增大;在力矩载荷作用下,钢球与保持架的作用力随着力矩载荷的增大先增大再减小而后急剧增大;增大保持架兜孔间隙与外沟曲率半径系数有利于减小钢球与保持架的作用力。

角接触球轴承内圈织构设计及对油气润滑两相流的影响

针对角接触球轴承油气润滑中内圈润滑油含量少和保持性差的问题,提出在轴承内圈滚道设计圆凹坑形表面织构的润滑增效方法。基于气液两相流模型和多重参考系方法,建立内圈织构化角接触球轴承腔内油气两相流数值分析模型,分析内圈织构对轴承油气两相流动及润滑增效的影响。结果表明:织构化轴承可以显著提高润滑油在内圈的保持量,同时改善轴承腔内润滑油分布不均的状况;在微织构附近油气两相流动更不规则,所产生的压力梯度和速度梯度有利于提高气液两相膜的承载力;随着轴承转速的升高,内圈织构润滑增效效果相对减弱;随着供油量的增加,内圈织构润滑增效效果更加显著。

考虑滚动体滑移的全陶瓷角接触球轴承非线性动态特性分析

为了探究陶瓷滚动体发生滑移运动时全陶瓷角接触球轴承的动态特性,建立了滚动体与轴承外圈的接触模型,计算了滑移情况下的接触参数。在此基础上建立了考虑滚动体滑移行为的全陶瓷角接触球轴承动力学模型,通过模型的计算结果分析了轴承系统的振动特性和周期规律。由模型计算结果可知,滚动体发生滑移运动时接触变形和接触面积随载荷的增大而增大,然而接触变形远小于正常接触时的情况,接触面积大于正常接触时的情况。搭建了轴承转子试验台进行振动试验,在试验工况条件下得到的全陶瓷轴承振动幅值与模型计算的结果平均误差仅为0.68%,证明了模型的准确性。该研究为全陶瓷角接触球轴承的接触机理研究和动态特性分析提供了一定的理论依据。